Question

Two numbers are in the ratio 7:4. If their difference is 72, find the numbers
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Answer 1

Answer :

• The numbers are 168 and 96

Given :

• Two numbers are in the ratio is 7:4
• Difference is 72

To find :

• The numbers

Solution :

• Let the first number be 7x
• Let the second number be 4x

Given that, the difference is 72 so,

According to Question,

》7x - 4x = 72

》3x = 72

》x = 72/3

》x = 24

Then,

• First number = 7x = 7(24) = 168
• Second number = 4x = 4(24) = 96

Hence, The numbers are 168 and 96

Verification :

》7x - 4x = 72

》7(24) - 4(24) = 72

》168 - 96 = 72

》72 = 72

Hence verified

Answer 2

$\mathfrak {Given}\begin{cases} \sf \: Two \: numbers \: are \: in \: the \: ratio \: \bold{7 : 4}. \\ \\ \sf Difference \: of \: those \: numbers \: is \: \bold{72}.\end{cases}$

Need to find : Those numbers.

⠀⠀⠀⠀⠀⠀____________________

Let the numbers be 7k and 4k respectively.

$\: \:$

It is given that their difference is 72.

$\: \:$

$\mathfrak{ \underline{ \bigstar \: substituting \: the \: values \: : }}$

$\:$

$\sf : \implies \: 7k - 4k = 72 \\ \\ \\ \sf : \implies3k = 72 \\ \\ \\ \sf : \implies \: k = \cancel\frac{72}{3} \\ \\ \\ \: \sf : \implies \underline{\boxed{\mathfrak\pink{k = 24}}} \: \bigstar$

$\: \:$

Now, put the value of k in the ratio.

$\: \:$

• First number = 7k = 7(24) = 168
• Second number = 4k = 4(24) = 96

⠀⠀⠀⠀⠀⠀____________________

$\sf\therefore{\underline{Hence, \: the \: two \: numbers \: are \: \bold{168} \: and \: \bold{96} \: respectively.}}$

$\: \:$

$\mathfrak {\underline{ \bigstar \: Verification \: :}}$

$\: \:$

$\sf : \implies \: 7k - 4k = 72 \\ \\ \\ \sf : \implies \: 3k = 72 \\ \\ \\ \sf : \implies3(24) = 72 \\ \\ \\ \sf : \implies72 = 72$

$\: \:$

⠀⠀⠀⠀⠀⠀____________________

$\sf\therefore{\underline{Hence, \: verified \: \: }}$